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Pentellated 8-simplexes

In eight-dimensional geometry, a pentellated 8-simplex is a convex uniform 8-polytope with 5th order truncations of the regular 8-simplex. There are two unique pentellations of the 8-simplex. Includin

Uniform 8-polytope

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets. A uniform

Runcinated 8-simplexes

In eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-simplex. There are eleven unique runcinations of the 8-si

1 33 honeycomb

In 7-dimensional geometry, 133 is a uniform honeycomb, also given by Schläfli symbol {3,33,3}, and is composed of 132 facets.

7-demicubic honeycomb

The 7-demicubic honeycomb, or demihepteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 7-space. It is constructed as an alternation of the regular 7-cubic honeycom

E8 polytope

In 8-dimensional geometry, there are 255 uniform polytopes with E8 symmetry. The three simplest forms are the 421, 241, and 142 polytopes, composed of 240, 2160 and 17280 vertices respectively. These

3 31 honeycomb

In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol {3,3,3,33,1} and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around

Stericated 8-simplexes

In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simpl

Cyclotruncated 7-simplex honeycomb

In seven-dimensional Euclidean geometry, the cyclotruncated 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, truncated 7-simplex, bitrunca

Hexicated 8-simplexes

In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex.

Cantellated 8-simplexes

In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex. There are six unique cantellations for the 8-simplex, including pe

Omnitruncated 7-simplex honeycomb

In seven-dimensional Euclidean geometry, the omnitruncated 7-simplex honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 7-simplex facets. The facets of

4 21 polytope

In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it

Truncated 8-simplexes

In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees of truncation. Vertices of the truncatio

8-cube

In geometry, an 8-cube is an eight-dimensional hypercube. It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells, 1120 tesseract 4-faces, 448 5-cube 5-faces, 112 6-cube 6-faces, and 16 7

7-cubic honeycomb

The 7-cubic honeycomb or hepteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 7-space. It is analogous to the square tiling of the plane and to the cubic ho

8-demicube

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed. It is part of a dimensionally infinite family of unifor

1 42 polytope

In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its bifurcating Coxeter-Dynkin diagram, with a single

A8 polytope

In 8-dimensional geometry, there are 135 uniform polytopes with A8 symmetry. There is one self-dual regular form, the 8-simplex with 9 vertices. Each can be visualized as symmetric orthographic projec

Rectified 8-cubes

In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube. There are unique 8 degrees of rectifications, the zeroth being the 8-cube

D8 polytope

In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, 64 are unique, and 127 are shared with the B8 symmetry. There are two regular forms, the 8-orthoplex, and 8-demicube with 1

8-orthoplex

In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 2

Truncated 8-orthoplexes

In eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex. There are 7 truncation for the 8-orthoplex. Vertices of the trunca

Heptellated 8-simplexes

In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex. There are 35 unique heptellations for

Rectified 8-orthoplexes

In eight-dimensional geometry, a rectified 8-orthoplex is a convex uniform 8-polytope, being a rectification of the regular 8-orthoplex. There are unique 8 degrees of rectifications, the zeroth being

Quarter 7-cubic honeycomb

In seven-dimensional Euclidean geometry, the quarter 7-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 7-demicubic honeycomb, and a quarter of t

Rectified 8-simplexes

In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex. There are unique 3 degrees of rectifications in regular 8-polytopes

2 41 polytope

In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its bifurcating Coxeter-Dynkin diagram, with a single

7-simplex honeycomb

In seven-dimensional Euclidean geometry, the 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, rectified 7-simplex, birectified 7-simplex,

Cantic 8-cube

In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube.

8-simplex

In geometry, an 8-simplex is a self-dual regular 8-polytope. It has 9 vertices, 36 edges, 84 triangle faces, 126 tetrahedral cells, 126 5-cell 4-faces, 84 5-simplex 5-faces, 36 6-simplex 6-faces, and

B8 polytope

In 8-dimensional geometry, there are 256 uniform polytopes with B8 symmetry. There are two regular forms, the 8-orthoplex and 8-cube, with 16 and 256 vertices respectively. The 8-demicube is added wit

Truncated 8-cubes

In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube. There are unique 7 degrees of truncation for the 8-cube. Vertices of the tru

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